Theorem mpteq1i 4739

Description: An equality theorem for the maps to notation. (Contributed by Glauco Siliprandi, 17-Aug-2020.)

Hypothesis

Ref	Expression
mpteq1i.1	|- A = B

Assertion

Ref	Expression
mpteq1i	|- ( x e. A |-> C ) = ( x e. B |-> C )

Distinct variable groups:   x, A   x, B

Allowed substitution hint:   C( x)

Proof of Theorem mpteq1i

Step	Hyp	Ref	Expression
1		mpteq1i.1	. 2 |- A = B
2		mpteq1 4737	. 2 |- ( A = B -> ( x e. A |-> C ) = ( x e. B |-> C ) )
3	1, 2	ax-mp 5	1 |- ( x e. A |-> C ) = ( x e. B |-> C )

Syntax hints:   = wceq 1483   |-> cmpt 4729

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-ral 2917  df-opab 4713  df-mpt 4730

This theorem is referenced by:  wlknwwlksnbij2  26778  wlkwwlkbij2  26785  wwlksnextbij  26797  limsupequzmptlem  39960  sge0iunmptlemfi  40630  sge0iunmpt  40635  hoidmvlelem3  40811  smfmulc1  41003  smflimsuplem2  41027